Tomographic imaging is well-known in the art, particularly through its commercial use in the X-ray spectrum. Tomography is generally defined as any of several techniques for making a detailed image of a predetermined plane section of a solid object while blurring out the images of other planes. Computed tomography typically compiles the plane sections into a three-dimensional, computer-generated image. X-ray computed tomography has become a ubiquitous medical technique for non-invasive diagnosis of medical conditions.
Standard tomographic methods require movement of the subject to be imaged relative to the radiation source. Typically the radiation source is rotated about an axis of the subject to image slices of the object, and the object is moved along the axis to capture the desired number of image slices to be compiled to form the tomographic image.
Fresnel Binary Lenses
Conventional lenses are based on refraction, while a Fresnel binary lens (sometimes referred to simply as a “Fresnel lens” or a “binary lens”) operates by diffraction. Fresnel lenses offer the ability to perform unique beam manipulation and frequency-dependant focusing.
A binary lens is a Fresnel zone plate with phase or amplitude patterns, which is formed by a series of concentric ring structures. The diffracted wave amplitude u(z) along the z-axis with the Fresnel binary lens can be written as
                              u          ⁡                      (            z            )                          =                              ∑            n                    ⁢                                          ⁢                                    A              n                        ⁢                                          ∫                ∫                            S                        ⁢                          exp              ⁡                              [                                                      ⅈ2π                    ⁡                                          (                                                                        n                                                      r                            p                            2                                                                          +                                                  1                                                      2                            ⁢                                                                                                                  ⁢                            λ                            ⁢                                                                                                                  ⁢                            z                                                                                              )                                                        ⁢                                      (                                                                  x                        2                                            +                                              y                        2                                                              )                                                  ]                                      ⁢                          ⅆ              x                        ⁢                          ⅆ              y                                                          (        1        )            where An=sin c(n/L), n is an integer and L=2M with M=1, 2, 3, . . . rp2 is the Fresnel zone period with the area dimension, s is the area of the binary lens, and λ is the wavelength.
FIG. 1 plots the phase profile versus the square of the radius of a binary lens with the origin at the lens center point. The phase shift Φ(r2) is a function of r2=x2+y2. The phase shift for each step is 2π/L, which corresponds to an etching depth of λ/L(nTHz−1). For an 8-level silicon lens at 1 THz, the etching depth step is 15.5 μm. N is the total number of zones.
If n/rp2+1/(2λzn)=0, a maximum diffraction intensity can be obtained at the focal point zn:
                                          z            n                    =                      -                                          r                p                2                                            2                ⁢                                                                  ⁢                λ                ⁢                                                                  ⁢                n                                                    ,                  n          =                      ±            1                          ,                  ±          2                ,        ⋯                            (        2        )            
The diffraction efficiency η is defined as:η=|A−1|2=sin c2(1/L).  (3)
As seen in Equation 3, the diffraction efficiency increases rapidly with the number of phase level L, and the calculated diffraction efficiency ηtheory versus L is shown in Table 1. For a binary lens with L=8, the diffraction efficiency reaches 95%, in contrast with a Al zone plate or a 2-level lens, which has 41% efficiency.
TABLE 12-LEVEL4-LEVEL8-LEVELAL ZONE PLATEηtheory41%81%95%41%
The first order focus with n=−1 is defined as the main focus with the focal length:
                                          f            v                    =                                    z                              -                1                                      =                                                            r                  p                  2                                                  2                  ⁢                                                                          ⁢                  λ                                            =                                                                                          r                      p                      2                                                              2                      ⁢                                                                                          ⁢                      c                                                        ⁢                  v                                ∝                v                                                    ,                            (        4        )            where c is the speed of light, and ν is the frequency of light. The focal length fv is linearly proportional to light frequency v. FIG. 2 schematically illustrates the frequency-dependent focal length of a binary lens with an incident plane wave. Two frequencies with ν1 and ν2 are focused at the focal points with the focal length f1 and f2, respectively. Because ν1=2ν2, then f1=2f2, as calculated using Equation 4.
For a single lens imaging system with paraxial ray approximation, the relationship between object distance z, image distance z′, and the focal length fv is governed by the imaging equation:
                                          1            z                    +                      1                          z              ′                                      =                              1                          f              v                                .                                    (        5        )            
If the image plane position is fixed (therefore z′ is fixed), for a wave with frequency ν, due to the frequency-dependent focal length fv, the object distance z is also frequency-dependent and z has the form:
                    z        =                                                            f                v                            ⁢                              z                ′                                                                    z                ′                            -                              f                v                                              =                                                                      r                  p                  2                                ⁢                                  z                  ′                                ⁢                v                                                              2                  ⁢                  c                  ⁢                                                                          ⁢                                      z                    ′                                                  -                                                      r                    p                    2                                    ⁢                  v                                                      .                                              (        6        )            Thus, at each frequency ν, there is a corresponding value of z such that a target at location z is imaged at the position z′. Unlike with conventional refractive imaging lenses, there is no contribution of the refractive index in Equation 6. The refractive index of a binary lens introduces Fresnel loss, but does not affect the focal length or image resolution.Terahertz (THz) Waves
The THz wave band occupies a large portion of the electromagnetic spectrum between the infrared and microwave band. Called ultra-Hertz waves in the 1920s, THz waves are an emerging frontier in imaging science and technology. Compared to the relatively well-developed medical imaging at microwave and optical frequencies, however, basic research, new initiatives, and advanced technology developments in the THz band have been limited to date. During the past decade, THz waves (also referred to as “T-ray” radiation) have been used to characterize the electronic, vibrational, and compositional properties of solid, liquid, and gas phase materials. THz waves are particularly well-suited for biomedical applications. Emerging T-ray tomographic methods are discussed in PCT Application No. PCT/US02/36279, incorporated herein by reference, titled TRANSMISSION MODE TERAHERTZ TOMOGRAPHY, filed by Rensselaer Polytechnic Institute on Nov. 13, 2002, naming Xi-Cheng Zhang, a co-inventor of the present invention, and others as inventors.
Lenses for THz Wave Systems
Lenses are a basic element in optical imaging systems. In imaging and Terahertz Time Domain Spectroscopy (THz TDS) technologies, T-ray focusing and collimating have mainly relied on parabolic mirrors, silicon lenses, and polyethylene lenses. For a broad THz beam, however, it is difficult, if not impossible, to fabricate silicon or polyethylene lenses with short focal lengths for large numerical apertures. For two-dimensional (2D), charged coupled device (CCD) THz imaging, it is very difficult to obtain a high quality THz image on a ZnTe sensor by using parabolic mirrors, due to their aberration and the difficulty of alignment. On the other hand, fabricating a 4-inch THz binary lens with a short focal length is relatively less difficult. Binary lenses are also much lighter and more compact than conventional THz optics. Despite these characteristics, binary lenses have not typically been used as THz diffraction optics for maneuvering the THz wave front.
To overcome the shortcomings of existing tomographic imaging systems and methods, a new system and method are provided. Incorporated in the system and method are the use of Fresnel lenses and the terahertz (THz) frequency range. An object of the present invention is to provide an improved tomographic imaging system and method that permit the tomographic image to be obtained without rotating or moving the target relative to the radiation source. Related objects will be evident from the summary and detailed description of the invention provided below.